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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle ) is equal to the sum of the areas of the squares on the other two sides.
Ebook version, in PDF format, full text presented. The Pythagorean Theorem: A 4,000-Year History, 2007, Princeton University Press, ISBN 978-0-691-12526-8; The Facts on File Calculus Handbook (Facts on File, 2003), 2005, Checkmark Books, an encyclopedia of calculus concepts geared for high school and college students; Music by the Numbers ...
The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). Although Pythagoras is most famous today for his alleged mathematical discoveries, [132] [207] classical historians dispute whether he himself ever actually made any significant contributions to the field.
Since the diagonal of a rectangle is the hypotenuse of the right triangle formed by two adjacent sides, the statement is seen to be equivalent to the Pythagorean theorem. [8] Baudhāyana also provides a statement using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle:
Xuan tu or Hsuan thu (simplified Chinese: 弦图; traditional Chinese: 絃圖; pinyin: xuántú; Wade–Giles: hsüan 2 tʻu 2) is a diagram given in the ancient Chinese astronomical and mathematical text Zhoubi Suanjing indicating a proof of the Pythagorean theorem. [1] Zhoubi Suanjing is one of the oldest Chinese texts on mathematics. The ...
The Zhoubi is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem. It claims to present 246 problems worked out by the Duke of Zhou as well as members of his court, placing its composition during the 11th century BC.
Bhaskaracharya proof of the pythagorean Theorem. Some of Bhaskara's contributions to mathematics include the following: A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a 2 + b 2 = c 2. [21] In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations ...
[7] The interest in the question may suggest some knowledge of the Pythagorean theorem, though the papyrus only shows a straightforward solution to a single second degree equation in one unknown. In modern terms, the simultaneous equations x 2 + y 2 = 100 and x = (3/4) y reduce to the single equation in y : ((3/4) y ) 2 + y 2 = 100 , giving the ...